Rare-earth-based chalcogenides and their derivatives: an encouraging IR nonlinear optical material candidate

With the continuous development of laser technology and the increasing demand for lasers of different frequencies in the infrared (IR) spectrum, research on infrared nonlinear optical (NLO) crystals has garnered growing attention. Currently, the three main commercially available types of borate materials each have their drawbacks, which limit their applications in various areas. Rare-earth (RE)-based chalcogenide compounds, characterized by the unique f-electron configuration, strong positive charges, and high coordination numbers of RE cations, often exhibit distinctive optical responses. In the field of IR-NLO crystals, they have a research history spanning several decades, with increasing interest. However, there is currently no comprehensive review summarizing and analyzing these promising compounds. In this review, we categorize 85 representative examples out of more than 400 non-centrosymmetric (NCS) compounds into four classes based on the connection of different asymmetric building motifs: (1) RE-based chalcogenides containing tetrahedral motifs; (2) RE-based chalcogenides containing lone-pair-electron motifs; (3) RE-based chalcogenides containing [BS3] and [P2Q6] motifs; and (4) RE-based chalcohalides and oxychalcogenides. We provide detailed discussions on their synthesis methods, structures, optical properties, and structure–performance relationships. Finally, we present several favorable suggestions to further explore RE-based chalcogenide compounds. These suggestions aim to approach these compounds from a new perspective in the field of structural chemistry and potentially uncover hidden treasures within the extensive accumulation of previous research.

0][41][42][43][44][45][46][47][48][49][50][51][52][53] Firstly, it should crystallize in a noncentrosymmetric (NCS) space group, which is a prerequisite for being a NLO crystal.Secondly, it should have a large d eff value, preferably more than 4 pm V −1 (but even better if it exceeds 8 pm V −1 ), in order to enhance the conversion efficiency.Additionally, it should have a high LIDT to withstand high power densities of fundamental frequency light waves.The LIDT is positively correlated with the band gap (E g ), which should be at least 3.0 eV, but it is even more desirable for it to be above 3.5 eV.Furthermore, the crystal should possess moderate birefringence (Dn) falling within the range of 0.03-0.10.Excessive birefringence can lead to the walk-off effect, while a small birefringence is not conducive to achieving phase-matching (PM).In addition, the crystal should have a wide optical transparency range that encompasses two signicant atmospheric windows: 3-5 mm and 8-12 mm.Finally, the perfect IR-NLO crystal should exhibit stable physical and chemical properties, maintaining stability even when exposed to the air.It should also demonstrate thermal stability, which is advantageous for growing large-sized crystals.Among the various families of materials, chalcogenides show promising potential as excellent candidates for IR-NLO crystals.Extensive research has been conducted on these materials, demonstrating their ability to achieve a superior balance between d eff and E g compared to other families.
Rare-earth (RE)-based chalcogenides, which are a subset of chalcogenides, continue to garner attention from researchers due to the unique properties of lanthanide elements.According to Pearson's hard and so acid-base theory, 54 RE 3+ cations are categorized as hard bases.As a result, the bonds formed between these cations and anions exhibit a certain degree of ionic character, similar to alkaline earth metal cations.Additionally, the covalent nature of these bonds is primarily derived from the outer 5d and 6s orbitals.The 4f orbitals situated in the inner shell receive shielding from the outer 5s and 5p electrons, limiting their contribution to bonding.As the atomic number increases, the 4f orbitals become more dispersed, causing these electrons to not fully occupy the inner regions of the 5s and 5p orbitals.This incomplete shielding effect on the nucleus results in the phenomenon known as lanthanide contraction.Consequently, the ionic radii of Sc 3+ and Y 3+ are similar to those of Lu 3+ and Er 3+ in the lanthanide series, hence, Y is classied as a member of the RE elements.
Due to the relatively large size of RE 3+ cations, they can accommodate higher coordination numbers.Their common coordination numbers are typically less than or equal to 9, approaching the sum of the 6s, 6p, and 5d orbitals, and can even reach up to 12.This complexity in coordination numbers contributes to the diverse geometric congurations of their polyhedra.The combination of the high coordination numbers and moderate positive charge of RE 3+ cations enables them to effectively disperse excess negative charges on anionic groups.This dispersion reduces the mutual attraction between anionic groups, presenting an opportunity to obtain low-dimensional anionic framework materials.
So far, numerous reviews on IR-NLO materials have been published.While there are a few examples involving a small amount of RE-based materials, [55][56][57][58][59][60][61][62][63][64][65][66][67] there has been no systematic overview analyzing and summarizing the fascinating RE-based chalcogenide family.In order to better illustrate the advantages of RE-based chalcogenide compounds and address the challenges in this eld, this paper provides detailed explanations for 85 representative examples out of over 400 NCS compounds.  Thesexamples are categorized into four groups based on the various asymmetric building motifs: (1) REbased chalcogenides containing tetrahedral motifs; (2) REbased chalcogenides containing lone-pair-electron motifs; (3) RE-based chalcogenides containing [BS 3 ] and [P 2 Q 6 ] motifs; and (4) RE-based chalcohalides and oxychalcogenides.Finally, the conclusions and perspectives for RE-based chalcogenides and their derivatives are provided for further exploration.

RE-based chalcogenides containing tetrahedral motifs
Spontaneous self-aggregation of a single [MQ 4 ] anion disperses negative charges and increases the likelihood of acquiring a high-dimensional framework.RE cations exhibit excellent abilities to disperse negative charges, resulting in the formation of RE-Q bonds when charges are transferred to the anion.This creates favourable conditions for the generation of lowdimensional anionic frameworks.Additionally, the charge transfer optimizes the distribution of electrons in the compound, contributing more effectively to the NLO effects under the synergistic action of the polyhedral [REQ n ] and tetrahedral [MQ 4 ] asymmetric building motifs.In the La 3 -LiM IV S 7 (M IV = Ge and Sn) system, the presence of a closed-ring structure for La-S-M IV reveals the existence of d-p p bonds attributed to the La-5d orbitals and S-3p orbitals.However, the empty 5d orbitals of La 3+ lack additional 5d electrons to form dp back-bonding p bonds.As a result, the formation of extra bonds between RE 3+ and Q 2− is hindered, limiting the enhancement of induced dipole moment oscillations.On the other hand, the lack of d electrons can be seen as an advantage as it avoids d-d and f-f transitions and enables better absorption of light.Next, the twelve systems containing tetrahedral motifs are introduced.
2.1.1.RE 3 GaS 6 (RE = Y, Dy, Ho, and Er).The crystal structure of RE 3 GaS 6 (RE = Dy, Y, Ho, and Er) was rst reported in 1971 based on powder XRD data. 68However, the linear and NLO properties of these compounds were not systematically studied and reported by Guo's group until 2013 69 and 2021, respectively. 70High-quality single crystals of RE 3 GaS 6 were obtained through solid-state reactions with KI as a ux.These chalcogenides are isomorphic and adopt the orthorhombic space group Cmc2 1 .The structures consist of two types of functional primitives: [RES 7 ] monocapped trigonal prisms and [GaS 4 ] tetrahedra.The overall structure can be described as [RES 7 ] functional primitives constructing a 3D network, with Ga atoms occupying the tetrahedral cavities (see Fig. 1).Each tetrahedral cavity is formed by 10 [RES 7 ] units, with 3 sharing an S-edge and 7 sharing an S-corner with the Ga atom.
The results of the SHG test indicate that the [RES 7 ] functional primitives play a key role in the NLO activity, in addition to the [GaS 4 ] tetrahedron.The d eff of RE 3 GaS 6 increases as the Shannon ionic radius of the RE 3+ ion decreases, namely, in the approximate sequence Dy 3 GaS 6 < Ho 3 GaS 6 z Y 3 GaS 6 < Er 3 GaS 6 when irradiated under a 2100 nm laser.This increase in d eff can be attributed to the increasing covalent bond feature of the RE-S bonds.Upon comparing the calculation results for RE 3 GaS 6 , it can be concluded that the frontier orbitals of all compounds are primarily inuenced by the RE element and S, with very little involvement of Ga.Additionally, the calculated SHG coefficients for these suldes closely match their experimental d eff .Furthermore, the calculated value of Dn, which determines the phase-matchability of IR-NLO materials, is also in line with experimental PM behaviors.
2.1.2.Eu 8 Sn 4 Se 20 .As a member of the (M II 2 M IV Q 5 ) n family (M II = divalent metals, Eu, Yb, Pb, and Sn; M IV = group 14 metals; Q = S, Se, and Te; n = 1, 2, and 4), Eu 8 Sn 4 Se 20 is the rst material to demonstrate NLO activity, despite the presence of some NCS structures within this system.Although the synthesis, structure, and optical E g of Eu 8 Sn 4 Se 20 were reported by Dorhout and colleagues in 2001, 71 its NLO performance was not reported until 2020 by Guo's group. 72he structure of Eu 8 Sn 4 Se 20 , which belongs to the orthorhombic space group P2 1 2 1 2, is displayed in Fig. 2a   (1 × a-SiO 2 in the range of 150-210 mm under 2010 nm laser radiation), although the intensity is not particularly promising.Dipole moment measurements indicate that the majority of the dipole moment vectors of Eu/Se are in opposite directions, resulting in smaller dipole moments.This could be the primary reason for the compound's weak SHG signals.
In EuCu 2 SiS 4 , there is 1 Eu, 1 Cu, 1 Si, and 2 S atoms in the crystallographically unique unit.This structure can be seen as a 3D network formed by [EuS 8 ] bicapped trigonal prisms, with Cu and Si atoms occupying the tetrahedral cavities (Fig. 3a ] tetrahedra through sharing vertexes, edges, and faces, respectively (Fig. 3c).
Although EuCu 2 M IV Q 4 (M IV = Si, Ge; Q = S, Se) belong to the NCS space groups, no apparent SHG signals were detected under the two most commonly used wavelengths of 1064 nm and 2100 nm.This result is completely different from the previously reported isomorphic compounds of alkaline earth metal groups with strong SHG signals, and the underlying mechanism is currently unclear.
2.1.4.RE 3 M 1−x M 0 Q 7 (RE = Y, La-Nd, Sm-Tm, Yb; M and M 0 = metals or metalloids; Q = S, Se).The compounds RE 3 -M 1−x M 0 Q 7 , which represent a large and well-known class of chalcogenides (>400 compounds), have been extensively studied due to their intriguing structural chemistry and technologically relevant physical properties.  From chemical perspective, the RE 3 M 1−x M 0 Q 7 series can be seen as derivatives of the classic parent structure of ternary Ce 3 Al 0.67 S 7 , 193,194 achieved through a chemical co-substitution route.In this study, two examples are presented as structural prototypes within the RE 3 M 1−x M 0 Q 7 family: the La 3 CuSiS 7 -type structure (Fig. 4a) and the La 3 FeGaS 7 -type structure (Fig. 4b).In these structures, the M and M 0 cations are located at specic sites and are limited to certain types of cations.For example, M can be located with different metal ions with various valence states, like monovalent IA and IB elements (with 100% occupancy), bivalent IIA, IIB, and transition-metal elements (with 50% occupancy), or occasionally trivalent IIIA elements (with sectional occupancy).M 0 , on the other hand, is typically associated with tetravalent IVA elements. The locl coordination of M, situated at the 2a Wyckoff position, is either in a trigonal [MQ 3 ] or an octahedral/ trigonal antiprismatic [MQ 6 ] conguration, while M 0 , located at the 2b Wyckoff position, exhibits a tetrahedral [M 0 Q 4 ] coordination.
It is worth mentioning that the compounds in this family exhibit signicantly different SHG intensities, the underlying reasons for which have not been revealed.In 2015, Chen's research group provided an unprecedented explanation for the unique atomic distribution within this family, which is observed on both the octahedral 2a and tetrahedral 2b sites.This distribution is a direct consequence of the combined considerations of total energy and charge balance.What is even more intriguing is that, in the case of the RE 3 M 1−x M 0 Q 7 family, the atomic distribution predominantly determines the NLO properties.Consequently, members exhibiting a high d eff value should adhere to the formula RE 3 M 0.5 M IV Q 7 .
Recently, Wu's group discovered a series of new isomorphic compounds, RE 3 LiMS 7 .Compared with the previously reported NPM behavior, these compounds exhibit useful PM features.Among them, La 3 LiGeS 7 and La 3 LiSnS 7 show strong d eff values (0.7 and 1.2 × AgGaS 2 , respectively) and large LIDTs (6.0 and 2.5 × AgGaS 2 , respectively).Detailed theoretical calculations indicate that the d eff values of the RE 3 LiMS 7 family originate from the cooperation of intrinsic dipole moments and d-p delocalized-p-electron-induced dipole oscillations.
2.1.5.EuM II M IV Q 4 (M II = Cd, Hg; M IV = Ge, Sn; Q = S, Se).It is well known that tetrahedral [MQ 4 ] functional primitives, such as [M IV Q 4 ] and [M II Q 4 ], make a large contribution to the SHG effect.Additionally, the introduction of two or more asymmetric building units helps in further modulating the crystal structure to obtain materials with SHG activities.6][197][198][199][200][201][202] Considering that Eu 2+ and AE 2+ have similarities in their ionic radii and coordination conguration in metal chalcogenides, Kang's group successfully synthesized EuCdGeQ 4 in 2019, which was the rst example containing a RE element in this family. 132Subsequently, they introduced Hg 2+ with high polarizability to improve the d eff effect in the system, successfully obtaining two Hg-based compounds, EuHgGeSe 4 and EuHgSnS 4 . 133uM II M IV Q 4 (M II = Cd, Hg; M IV = Ge, Sn; Q = S, Se) are isostructural and crystallize in the NCS orthorhombic Ama2 space group.As shown in Fig. 5 Owing to the structural traits that arrange the overall NLOactive motifs ([M II Q 4 ] and [M IV Q 4 ] units) in an orderly manner along a specic direction, all units exhibit strong d eff (approximately 2-4 × AgGaS 2 @2090 nm) along with type-I PM behaviour.Furthermore, theoretical calculations and local dipole moment analyses suggest the signicant contribution of distorted [M II Q 4 ] tetrahedra to the improved d eff .These results conrm the intriguing potential applications of these materials as IR NLO crystals.This work also indicates the feasibility of replacing AE elements with RE elements in the exploration of novel IR-NLO candidates.
It is worth mentioning that the number of terminal S atoms per formula plays a crucial role in determining the linkage of [GaS 4 ] and [GeS 4 ] functional primitives as well as the aggregation density of the anionic moieties.Theoretical analysis shows that RE cations narrow the E g but Li does not, and that all components affect the d eff through the electronic transitions from the S-3p state to the La/Eu/Li-S, Ga-S, and Ge-S antibonding states.This understanding may provide useful guidance for the further exploration and development of novel IR-NLO materials.Interestingly, the powder Eu 2 Ga 2 GeS 7 exhibits a large d eff (1.6 × AgGaS 2 @2050 nm) with type-I NPM features, a wide transparent range, and a large theoretical Dn.
2.1.7.Ba 2 REM III Q 5 (RE = Y, Ce, Nd, Sm, Gd, Dy, and Er; M III = Ga, In; Q = Se, Te).Twenty chalcogenides with the formula Ba 2 REM III Q 5 were reported in 2012 and synthesized by Wu's group using a solid-state reaction. 135,136They aimed to introduce f-block and p-block elements into chalcogenides to obtain unique structures and physical properties.In addition, AE metals were added to increase the E g of the chalcogenides.
According to the report, the Ba 2 REGaSe 5 (RE = Y, Nd, Sm, Gd, Dy, and Er) and Ba 2 REGaTe 5 (RE = Sm and Gd) compounds are isomorphic, with a centrosymmetric triclinic system in the P 1 space group.On the other hand, the Ba 2 REInSe 5 (RE = Y, Nd, Sm, Gd, Dy, and Er), Ba 2 REGaTe 5 (RE = Y, Dy, and Er), and Ba 2 REInTe 5 (RE = Y, Ce, Nd, Sm, Gd, Dy, and Er) compounds belong to an NCS orthorhombic system in the Cmc2 1 space group.This discussion will focus solely on the NCS compounds.Fig. 7 shows the structure of the NCS Ba 2 REM III Q 5 compounds.The structure consists of 1D [REM III Q 5 ] 4− chains formed by two types of chains connected through shared Q atoms.These two types of chains are constructed by [REQ 6 ] octahedra and link together through shared edges, whereas [M III Q 4 ] tetrahedra connect through shared vertices.
Experimental results reveal that the d eff value of Ba 2 InYSe 5 is similar to that of AgGaSe 2 , making it the largest value among the compounds in this family.The Ba 2 REInSe 5 (RE = Gd, Er) compounds exhibit very weak SHG responses, while the Nd, Sm, and Dy compounds show undetectable SHG responses.The detection of weak SHG signals or the failure to detect signals in the compounds of this system may be attributed to the absorption of fundamental and harmonic light by the sample.4][205] On the other hand, it is evident that in the Ba 2 REInSe 5 compounds, the RE metal cation does not impact the crystal structure but does affect the intensity of the d eff .
2.1.8.Ba 4 RE 2 Cd 3 S 10 (RE = Sm, Gd, and Tb).Ba 4 RE 2 Cd 3 S 10 (RE = Sm, Gd, and Tb) is the only type of AE/RE/TM/Q (AE = alkaline earth elements; RE = rare-earth elements; M = main group elements; TM = d-block transition elements; and Q = chalcogen) system with an NCS space group.Previous reports on this system mainly focused on its magnetism. 206However, in 2022, Zhu's research group conducted a systematic investigation of its linear and NLO properties for the rst time. 137he preparation of the at needle transparent-brown crystals of Ba 4 RE 2 Cd 3 S 10 involved a solid-phase method of elemental mixtures in a KCl/BaCl 2 (1 : 3) ux at 1173 K.All of them are isostructural and adopt the NCS orthorhombic space group Cmc2 1 (no.36).Fig. 8 displays a view of the structure of Ba 4 -RE 2 Cd 3 S 10 on the bc plane, where the most prominent feature is the 2D complex anionic [RE 2 Cd 3 S 10 ] 8− layers stacked in an ABABAB fashion along the ab-plane, with discrete Ba 2+ cations located in between.
Remarkably, Ba 4 Sm 2 Cd 3 S 10 exhibits a strong d eff (1.8 × AgGaS 2 ) and a signicantly higher LIDT (14.3 × AgGaS 2 ).This is the rst case of a quaternary AE/RE/TM/Q system possessing an IR-NLO property.Furthermore, the theoretical results for the structure-activity relationships suggest that the combined action of different types of NLO-active motifs (i.e., [RES 6 ] and [CdS 4 ]) contributes to the SHG activity.
2.1.9.LaAEM III 3 S 7 (AE = Sr, Ca; M III = Al, Ga).LaCaGa 3 S 7 was rst synthesized in 1987, and only its structure was reported at that time. 138In 2022, Zhang's team synthesized LaAEGa 3 S 7 (AE = Ca, Sr) again in a study that compared their specic properties and revealed a series of changes in analogues involving oxides, suldes, and oxysuldes. 139Subsequently, they obtained two other isomorphic LaAEAl 3 S 7 (AE = Ca, Sr) compounds through homologous substitution. 140AEM III 3 S 7 adopt the P 42 1 m space group of the tetragonal system.In the structure, La and AE atoms co-occupy the same position with occupation ratios of 50% and 50%.As shown in     perfectly balanced properties for IR-NLO chalcogenides: the largest d eff among all reported thiosilicates (2.0 and 2.1 × AgGaS 2 @2050 nm for LaLiSiS 4 and CeLiSiS 4 , respectively) with PM ability, high LIDTs (14 and 9 × AgGaS 2 @1064 nm), large E g (3.71 and 2.92 eV), wide IR transmission window (0.35-18 mm), and good thermal stability above 973 K.This study not only enriches the structural chemistry of RE-based thiosilicates, but also offers an efficient method to design novel highperformance IR-NLO candidates.
KREM IV Q 4 compounds (RE = Y, La-Nd, Eu-Tb; M IV = Si, Ge; Q = S, Se) belong to the NCS monoclinic space group P2 1 (no.4) and are isostructural.Therefore, for the purposes of this description, only the structure of KYGeS 4 will be detailed as a representative.This compound was successfully synthesized in 2021 by Mei's group using a charge transfer engineering strategy.Fig. 11b shows that the [YS 7 ] and [GeS 4 ] motifs are interconnected by sharing polyhedral edges, and the [YS 7 ] units are linked to one another through sharing vertexes to generate the innite 2D [YGeS 4 ] n layers.The interlayer interstices are lled by K + cations to maintain charge balance.It is noteworthy that both [GeS 4 ] and [YS 7 ] polyhedra are uniformly arranged along the ab plane, which facilitates the positive superposition of microscopic second-order susceptibility, resulting in a strong d eff .KYGeS 4 overcomes the E g limitation found in rare earth chalcogenides with the largest E g (3.15 eV) within this material system, while displaying a signicant d eff (ca.1.0 × AgGaS 2 ).Moreover, KYGeS 4 is the rst RE-based chalcogenide to surpass the "3.0 eV wall" observed in IR-NLO crystals.
Isostructural AREM IV Q 4 compounds (RE = La-Nd, Eu-Yb; M IV = Si, Ge; Q = S, Se) were synthesized by Loye and co-workers using a molten alkali halide ux growth method in 2019.All of them adopt the NCS monoclinic space group P2 1 2 1 2 1 (no.19), and in this discussion, we will focus on the structure of CsLaGeS 4 as an example.CsLaGeS 4 can be easily obtained by adding Ge to the reaction mixture of La 2 S 3 and S in the CsCl/KCl eutectic ux.In the structure of CsLaGeS 4 , there are [LaS 7 ] monocapped trigonal prisms and [GeS 4 ] tetrahedrons.These polyhedral [LaS 7 ] motifs and tetrahedral [GeS 4 ] units interlink together through the sharing edge to generate the innite 2D [LaGeS 4 ] − slabs in the ac plane.The Cs + cations ll in the gaps between the layers and act as charge balancers.Unfortunately, only CsLaGeS 4 was found to be SHG-active, exhibiting nearly half the intensity of a-SiO 2 when irradiated with a Nd:YAG 1064 nm laser.This compound also behaves as a semiconductor with an E g of 3.60 eV based upon UV-vis diffuse reectance measurements.
2.1.12.K 3 REP 2 S 8 (RE = Y, Ho, and Er).In 2023, a new series of RE-based thiophosphates, K 3 REP 2 S 8 , was successfully prepared and systematically investigated by Wu and coworkers. 149Microcrystals of K 3 REP 2 S 8 were obtained with the stoichiometric K, RE 2 S 3 , P, and S by spontaneous crystallization.Single-crystal XRD structural renement indicates that K 3 REP 2 S 8 adopts two different types of space groups: NCS P2 1 (RE = Y, Ho, and Er) and CS P2 1 /c (RE = Pr, Sm, and Gd).The similarities and differences in their structures are as follows: (i) they possess the same asymmetric motifs consisting of 3 K, 1 RE, 2 P, and 8 S sites but different Z values (Z = 2 for NCS; Z =  Chemical Science Review

RE-based chalcogenides containing lone-pair-electron motifs
The unique structural characteristics of polyhedra formed by cations that contain a stereochemically active lone pair (SCALP) give rise to a strong local built-in electric eld, resulting in a signicant dipole moment.8][209][210][211][212][213][214] The inclusion of highly positively charged RE cations effectively creates a built-in electric eld within their immediate surroundings.This takes advantage of the electrostatic interaction between the SCALP electrons and the RE cations to align the initially different orientations, thereby facilitating the macroscopic overlap of the static dipole moments.However, Nd 8 Sb 2 S 15 could not be obtained as a single phase. 151Although Pr 8 Sb 2 S 15 had previously been obtained in 1981, its SHG performance was not reported. 152In 2017, Zhao obtained Ce 8 Sb 2 S 15 via high-temperature solid-state synthesis. 153The lanthanide contraction from La to Nd does not affect the crystal structure of these compounds, as they are isostructural and adopt the NCS tetragonal I4 1 cd space group.The structure of RE 8 Sb 2 S 15 with the unit cell outlined is shown in Fig. 13a.The structure consists of discrete [SbS 3 ] 3− trigonal pyramids arranged approximately along the [001] direction, lled by RE 3+ cations and S 2− anions.RE 1 and RE 2 have normal monocapped trigonal prismatic coordination environments, whereas the other two crystallographically unique RE positions, RE3 and RE4, are occupied in approximately square antiprismatic modes (Fig. 13b).Therefore, the formula of RE 8 Sb 2 S 15 can be written as The compound La 8 Sb 2 S 15 shows an E g of 2.30 eV and a high effective d eff of 1.2 × AgGaS 2 (at 74-106 mm under 2050 nm laser irradiation) with NPM behavior.However, no signicant d eff was observed for Pr 8 Sb 2 S 15 , which may be linked to its poor crystallinity.
2.2.2.La 2 CuSbS 5 .A millimeter-grade single crystal of La 2 -CuSbS 5 was rst prepared by Zhu's group in 2019 using a BaCl 2 / CsBr ux at a temperature of 1273 K. 154 Although this compound was discovered in 2016, no properties were reported at that time due to the inability to obtain a pure phase. 155ingle-crystal XRD result indicated that La 2 CuSbS 5 belongs to the NCS orthorhombic system with the space group Ima2 (no.46).The structure of La 2 CuSbS 5 made of several distinct units, namely, [LaS 10 ] polyhedra, [CuS 4 ] tetrahedra, and [SbS 4 ] pyramids.Fig. 14a depicts the projection of La 2 CuSbS 5 viewed down the ab plane.The 3D network is constructed from two types of 2D layers (La/Cu/S and La/Sb/S) that are interconnected through shared S-S apexes and edges.The detailed coordination environment of the La atoms is shown in Fig. 14b.
Moreover, La 2 CuSbS 5 can be seen as a result of the stereochemically active lone pair induction (SCALPI) strategy, which is based on the previously known CS La 2 CuInS 5 .Investigation into its optical properties showed that La 2 CuSbS 5 displays a suitable PM d eff (0.5 × AgGaS 2 ) and a large LIDT (6.7 × AgGaS 2 ), making it a promising candidate for IR-NLO materials.Furthermore, theoretical calculations support the notion that the d eff can be attributed to the synergistic effects of the functional primitives, with a particular emphasis on the [SbS 4 ] motifs.7][158][159][160][161][162] As shown in Fig. 15, the structures of these compounds have both similarities and differences.Firstly, the isostructural Ga-analogues belong to the orthogonal system [space group: Aba2 (no.41)], while the isostructural In-analogues crystallize in the tetragonal system [space group: P4 1 2 1 2 (no.92) or P4 3 2 1 2 (no.96)].Secondly, they have similar asymmetric motifs consisting of 4 The theoretical results suggest that the SHG response of RE 4 GaSbS 9 can be attributed to the electronic transitions from the S-3p states in the valence bands to the Sb-S and RE-S antibonding states.On the other hand, the SHG response of RE 4 InSbQ 9 is attributed to the thermal vibrations of the lattice.

RE-based chalcogenides containing [BS 3 ] and [P 2 Q 6 ] motifs
The [BS 3 ] motif, with its distinctive planar conjugated p 4 6 electron structure, is a crucial functional unit.Its introduction not only benets the synergistic enhancement of NLO response and LIDT, but also has a signicant impact on birefringence.By anchoring RE cations to the [BS 3 ] unit, the arrangement of the [BS 3 ] unit is optimized.The bonding interaction between them synergistically enhances the contribution to conductive bands, reinforcing the contribution to the empty virtual-hole transition process by the low-lying 4f or 5d orbitals in the rare earth ions and the p* anti-bonding orbitals of the [BS 3 ] unit.For the crossed ethane conguration of the [P 2 Q 6 ] unit, the 6 exposed Q atoms serve as sites to balance its negative charge through chemical bonding.The high coordination number of rare earth ions precisely matches this unit, allowing one RE cation to bond with one or even multiple [P 2 Q 6 ] units.This maximizes the functionality of this basic unit and synergistically enhances the NLO effects in conjunction with [REQ n ] polyhedra.In the following discussion, four systems are introduced: REBS 3 (RE = La, Ce, Pr, Nd, Sm, and Tb), Ca 2 RE(BS 3 )(SiS 4 ) (RE = La, Ce, and Gd), Eu 2 P 2 S 6 , and KREP 2 Se 6 (RE = Sm, Tb, and Gd).acting as a ux. 167They successfully synthesized REBS 3 in 2023.
In the same year, Mao's group proposed another method to obtain LaBS 3 by employing La 2 S 3 , B, S, and Li 2 S as a ux and characterized its structure and NLO properties. 168EBS 3 (RE = La, Ce, Pr, Nd, Sm, and Tb) are isomorphic and adopt an orthorhombic Pna2 1 space group.LaBS 3 can serve as an example to discuss the crystal structure; as shown in Fig. 16, its structure comprises triangular [BS 3 ] 3− units, with each La atom connecting to 9 S atoms to link with the [BS 3 ] 3− units.Each [BS 3 ] 3− unit is linked to 6 La 3+ atoms, ultimately forming the entire 3D network structure.
As expected, LaBS 3 possesses a large E g of 3.18 eV, the highest d eff among ortho-thioborates (1.2 × AgGaS 2 at 2050 nm), an ultra-high LIDT of 14 × AgGaS 2 , a wide IR transmission range (0.35-25 mm), and exhibits PM behaviour.The results of theoretical calculations indicate that the [LaS 9 ] 15− groups and the p-conjugated [BS 3 ] 3− anions are the main sources of the SHG effect.In general, this research provides us with a new method to synthesize new NLO materials.
The compounds Ca 2 RE(BS 3 )(SiS 4 ) (RE = La, Ce, and Gd) are isostructural and crystallize in the hexagonal P6 3 mc space group.Fig. 17 illustrates the structure of Ca 2 RE(BS 3 )(SiS 4 ) along the ab plane.In this structure, the RE 3+ and Ca 2+ ions occupy the same site, referred to as the M site, with a ratio of 1/3 and 2/ 3, respectively.Each M site coordinates with 6 S atoms to form an [MS 6 ] polyhedron, which connects with isolated [BS 3 ] 3− and [SiS 4 ] 4− units along the c axis, resulting in the overall 3D structure of Ca 2 RE(BS 3 )(SiS 4 ).
Theoretical calculations indicate that the big d eff mainly stem from the synergy between the [RES 6 ], [BS 3 ], and [SiS 4 ] groups.These ndings not only expand the scope of research on chalcogenides but also offer a straightforward synthetic method for heteroanionic thioborates.
2.3.3.Eu 2 P 2 S 6 .Compared with common metal chalcogenides, chalcogenophosphates with NCS structures are very few and difficult to synthesize, so they are rarely found as IR-NLO candidate materials.Although the crystal structure of REbased chalcogenophosphate Eu 2 P 2 S 6 was reported as early as 1987, 170 its NLO performance was not reported by the Guo's research group until 2022.

Review Chemical Science
Yellow block crystals of Eu 2 P 2 S 6 were prepared through a high-temperature solid-phase method between stoichiometric Eu, P 2 S 5 , and S at 1233 K.It belongs to the monoclinic Pn space group.The structure of Eu 2 P 2 S 6 can be viewed as comprising bicapped-triangular-prism [EuS 8 ] and dimeric [P 2 S 6 ] functional primitives built into a 3D framework via 8 : 18 : 13 intergrowth (Fig. 18).
This rst IR-NLO RE-based chalcogenophosphate, Eu 2 P 2 S 6 , displays wonderful comprehensive optical properties, including a moderate PM d eff (0.9 × AgGaS 2 ), large LIDT (3.4 × AgGaS 2 ), and broad IR transparency region (0.49-15.4 mm).Based on the results of structural analysis and theoretical studies, the overall IR-NLO properties are attributable to the synergetic effect of [EuS 8 ] and [P 2 S 6 ] functional primitives.This study not only developed the rst RE-based chalcogenophosphate as an advanced NLO candidate, but also provided a representative example for the future discovery of high-performance RE-based IR-NLO chalcogenides.
2.3.4.KREP 2 Se 6 (RE = Sm, Tb, and Gd).Combining the merits of multiple oxidation states, strong covalent character of the P-Q bonds, and low melting points, Guo's group successfully combined metal chalcophosphates with RE-centered units that exhibit large polarization, resulting in the synthesis of KREP 2 Se 6 (RE = Sm, Tb, and Gd) in 2022. 172The synthesis was carried out using the M x O y -B-Q (M = metal; Q = S, Se) solidstate route, which had previously been used to prepare chalcogenides by Huang and Guo et al. 108 The rst RE-based selenophosphates KREP 2 Se 6 (RE = Sm, Tb, and Gd) belong to the monoclinic P2 1 space group.They are composed of a 2D [REP 2 Se 6 ] − layer with K + ions lling the spaces in between (Fig. 19).The [REP 2 Se 6 ] − layer is built by layers in which each bicapped-trigonal-prism [RESe 8 ] unit is linked to four [RESe 8 ] units by sharing edges and vertices.These [RESe 8 ] units also connect with 4 [P 2 Se 6 ] 4− units by sharing faces, edges, and corners.The co-vertices are arranged on one side, while the co-edges are arranged on the other.
As a result, KREP 2 Se 6 (RE = Sm, Tb, and Gd) exhibit a PM d eff effect ranging from 0.34 to 1.08 × AgGaS 2 at 2100 nm and a LIDT ranging from 1.43 to 4.33 × AgGaS 2 .The theoretical calculations suggest that the cooperation between [P 2 Se 6 ] and [RESe 8 ] plays a predominant role in the d eff .This research demonstrates that RE-based selenophosphates are a promising type of IR-NLO material.It not only enhances the understanding of crystal chemistry in RE-based chalcophosphates but also expands the range of potential applications for NLO materials.

RE-based chalcohalides and oxychalcogenides
0][231][232][233] Unlike traditional chalcogenides, the presence of heteroanionic groups combines the high polarizability of chalcogenides with the advantages of oxides and halides that have wide E g .RE-based chalcohalides and oxychalcogenides not only incorporate disparate anions but also feature the presence of salt-inclusion compounds.Below, eleven RE-based chalcohalides and oxychalcogenides are introduced.
2.4.1.La 6 Cd 0.75 Ga 2 Q 11.5 Cl 2.5 (Q = S, Se).Two novel quinary chalcohalides, La 6 Cd 0.75 Ga 2 Q 11.5 Cl 2.5 (Q = S, Se), with heteroanionic functional motifs were discovered in 2021 by Huang's group using LaCl 3 as a reaction-ux. 173Both compounds belong to the NCS space group P6 3 .Fig. 20a displays a schematic  diagram of La 6 Cd 0.75 Ga 2 Q 11.5 Cl 2.5 seen along the ac plane.In the structure, plane-linked 1D [Cd(Q/Cl) 6 ] chains are packed along the 6 3 axes, and the tetrahedral [GaQ 4 ] units are separated along the direction of the 3-fold rotation axes.Furthermore, the [La(Q/Cl) 6 Q] polyhedra form a 3D network structure in the ab plane through vertex-and edge-sharing as shown in Fig. 20b with the unit cell outlined.
Moreover, the introduction of various heteroanionic functional motifs with varying sizes and electronegativity increases the distortion of structural groups while keeping the structural symmetry.This enhances the polarity of the NLO-active motifs, resulting in a greater d eff .As expected, La 6 Cd 0.75 Ga 2 S 11.5 Cl 2.5 exhibits a large LIDT of 18.6 × AgGaS 2 @1064 nm and a strong d eff of 0.8 × AgGaS 2 @43-75 mm under 2050 nm laser irradiation.RE 3 AsS 5 X 2 (RE = La, Pr; X = Cl, Br).The NCS chalcohalide La 3 AsS 5 Br 2 with the monoclinic space group Cc (no.9), 174 which is isostructural to the previously reported Pr 3 AsS 5 -Cl 2 , 175 was successfully prepared using a salt ux growth method in 2023 by Wang's group.
The 3D network of RE 3 AsS 5 X 2 (RE = La, Pr; X = Cl, Br) is composed of [RE1S 5 X 3 ] bicapped trigonal prisms, [RE2S 5 X 3 ] bicapped trigonal prisms, [RE3S 7 ] capped trigonal prisms, and SACLP [AsS 3 ] trigonal pyramids, which are interconnected with each other (Fig. 21a).The coordination environment of the crystallographically independent RE atoms in the structure of RE 3 AsS 5 X 2 is provided in Fig. 21b.The electron localization function results conrmed that the arrangement of the [AsS 3 ] groups contributes to the NCS nature of RE 3 AsS 5 X 2 .

Review
Chemical Science with NLO activity. 177][236] (K 3 I)[REB 12 (GaS 4 ) 3 ] (RE = Sm, Gd) share the same structure and belong to the hexagonal chiral space group P6 3 22.In the asymmetric unit, there are 1 A, 1 X, 1 RE, 1 Ga, 2 B, and 2 Q positions.The crystal structure consists of two parts: the polycationic Due to the signicantly low yield for most compounds, the majority of samples in this system were unable to undergo sizedependent SHG measurements.For instance, the d eff of (K 3 I) [SmB 12 (GaS 4 ) 3 ] is approximately 0.3 times that of KDP when subjected to a 1940 nm laser.The small d eff can be attributed to the arrangement of the SHG-active groups in their structures, which hinders the improvement of macroscopic polarizabilities.2.4.6.YSeBO 2 .Due to the difficulty of their synthesis, chalcogenide borates have been rarely studied as IR-NLO candidate materials in the past.The second selenide borate, YSeBO 2 , was successfully discovered by Guo's group in 2020. 180Transparent rodlike crystals of YSeBO 2 with a large E g of 3.45 eV were prepared through a traditional solid-phase reaction between Y 2 O 3 , B 2 O 3 , B, and Se and additional KI used as the ux.

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YSeBO 2 adopts the orthorhombic polar space group Cmc2 1 , and the 3D structure is formed by the connection between [YO 3 Se 4 ] 11− pentagonal bipyramids and [BO 3 ] 3− planar triangles by sharing O edges (see Fig. 25).It is worth mentioning that the heteroanionic [YO 3 Se 4 ] 11− functional motif was rst discovered in the chalcogenide system.In addition, YSeBO 2 displays a weak d eff of about 0.2 × KDP (@150-210 mm) with PM features.Theoretical analysis shows that the Se-4p and Y-4d states play a major role in the origin of SHG.The contribution of the [BO 3 ] 3− planar triangles did not show any impact due to its unfavorable arrangement.
Eu 3 GeOS 4 belongs to the orthorhombic Pca2 1 space group.As displayed in Fig. 26, neighbouring [EuOS 6 ] mono-capped trigonal prisms are interlinked through sharing faces to form a 3D framework structure, with isolated [GeOS 3 ] tetrahedra occupying the cavities.In other words, without considering the Eu-O/S bonds, the crystal structure of Eu 3 GeOS 4 can also be considered a pseudo-0D structure.It is interesting to note that the coordination mode of the heteroanionic [EuOS 6 ] functional motif was discovered for the rst time in oxychalcogenides.
2.4.8.RE 3 NbS 3 O 4 (RE = Ce, Sm, Gd, Dy).A series of REbased oxysuldes RE 3 NbS 3 O 4 (RE = Ce, Sm, Gd, Dy) were systemically investigated.][184][185] The crystals of RE 3 NbS 3 O 4 were prepared through solid-phase reactions at 1273 K using       together, forming the 3D network (Fig. 29b).As a result, Eu 2 M II Ge 2 OS 6 (M II = Mn, Fe, and Co) display excellent IR-NLO performance with an E g of 2.11-2.40eV, a PM d eff of 0.3-0.5 × AgGaS 2 at 200-250 mm, and a large LIDT of 2.8-8.3 × AgGaS 2 .They proposed that these compounds have the potential to replace M II using Cu or other d-block metals and other substitutions within the same family.
2.4.11.REAEGa 3 S 6 O (RE = La, Pr, and Nd; AE = Sr, Recent studies have mainly focused on the individual performances of oxysuldes, but there has been little investigation into the comparisons in the specic properties and changes in a series of analogues including oxides, suldes, and oxysuldes.In order to address this gap, a series of REAEGa 3 S 6 O (RE = La, Pr, and Nd; AE = Sr, Ca) compounds were synthesized by Wu Review Chemical Science and co-works in 2022, along with their corresponding LaAEGa 3 O 7 oxides and LaAEGa 3 S 7 suldes, which served as reference materials. 128The aim was to systematically study the trends in the key properties from oxides to suldes to oxysuldes.All of the REAEGa 3 S 6 O oxysuldes belong to the P 42 1 m space group of the tetragonal system, and they are isostructural with LaAEGa 3 O 7 and LaAEGa 3 S 7 .Fig. 30 presents the unique structure of these compounds, which can be described as consisting of two functional modules: charge-balanced [RE/AE] 5+ cations and 2D [Ga 3 S 6 O] 5− Cairo pentagonal layers.The chargebalanced module is composed of [(RE/AE)S 7 O] groups that are connected through edge-and face-sharing interactions, forming a 2D [(RE/AE)S 7 O] n layer.On the other hand, the 2D layers can be seen as a combination of many 5-membered rings, with two [GaS 4 ] and three [GaS 3 O] units surrounding each ring.
In particular, REAEGa 3 S 6 O fullls the property balance requirements (e.g., wide E g : 3.21-3.27eV and PM d eff : 0.9-1.0 × AgGaS 2 ).This compound shows promise as a potential IR-NLO crystal, as it combines the advantages of LaAEGa 3 O 7 and LaAEGa 3 S 7 through heteroanion-oriented performance engineering.The structure-activity relationships reveal that the heteroanionic [(RE/AE)S 7 O] and [GaS 3 O] functional motifs are particularly promising for NLO activity, as they exhibit large cooperation in the origin of SHG.These ndings not only provide a clear understanding of the variation in properties from oxide to sulde to oxysulde, but also highlight the feasibility of using heteroanion-oriented design to develop novel NLO candidates with well-balanced performances.

Conclusions and perspectives
RE-based chalcogenides, with their unique electronic congurations, have been extensively discussed in the eld of IR-NLO for several decades, and there has been growing interest in recent years.According to incomplete statistics, there are over 400 compounds with non-centrosymmetric structures among RE-based chalcogenides.However, to date, there has not been a comprehensive review that systematically summarized these compounds.Therefore, this paper provided a summary analysis of their synthesis methods, structures, optical properties, and structure-property relationships.The results of the statistical analysis of these compounds are summarized in Tables 1-4 and Schemes 1-4.Additionally, some key ndings have been uncovered: (1) Due to the Gd discontinuity effect, there is a slight variation in the ionic radius of lanthanide elements, which leads to differences in their chemical and physical properties.

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Therefore, based on differences in electronic conguration, as well as physical and chemical properties, the elements preceding Gd are classied as light RE elements or ceriumgroup elements (La-Eu), while the remaining elements are classied as heavy RE elements (Gd-Lu, Y, and Sc).As shown in Scheme 1, light RE-based chalcogenide compounds have greater appeal than heavy ones.Based on the classication of light and heavy RE elements, an analysis of these compounds reveals that the probability of obtaining NCS compounds through the synthesis of light RE elements is 47.9% (excluding the radioactive Pm element), which is twice the average of heavy RE elements (20.0%).Furthermore, the NLO-active compounds in the light RE elements group account for a remarkable 70.7% of the total, which is also double the percentage found in the heavy group (29.3%).Of course, the price difference between light and heavy RE elements will also impact the synthesis and amount of research into the compounds.(2) These compounds can be divided into four categories based upon the number of elements: ternary (9, 10.6%), quaternary (62, 72.9%), quinary (13, 15.3%), and hexanary (1, 1.2%).Furthermore, in terms of the dimensionality of the crystal structure, there are 6 (7.1%) 0D compounds, 1 (1.2%) 1D compound, 22 2D (25.9%) compounds, 42 (49.4%)3D compounds, and 14 (16.5%)MD compounds.Additionally, based on the crystal systems, they can be divided into ve categories: monoclinic (12, 14.1%), orthorhombic (31, 36.5%),tetragonal (16, 18.8%), trigonal (2, 2.4%), and hexagonal (24, 28.2%).Analysis of the space group distribution revealed that

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structural chemistry and understanding the origin of their properties through additional experimental results.(4) For the synthesis method of RE-based IR-NLO compounds, the common method is high-temperature solid-state synthesis.Additionally, the introduction of RE elements not only involves the use of elemental RE, but also employs the reactive ux and boron-chalcogen mixture methods.The boron-chalcogen mixture method uses boron and RE oxides to remove oxygen in situ from rare earth oxides during the reaction, allowing the participation of RE elements.The emergence of this method enriches the selection of reaction pathways.
Currently, out of over 400 RE-based compounds, fewer than 100 demonstrate NLO properties.With decades of accumulated knowledge, our predecessors have laid a substantial foundation for us.Now is the opportune moment to strategically delve into synthesizing and exploring the underlying mechanisms, cultivating the soil to harvest successful outcomes.For this, the following outlook is provided: (1) Further investigation into the mechanisms of RE-based polyhedra is needed.Currently, a signicant question remains unanswered in the realm of RE-based compounds: why do only certain compounds of RE elements exhibit nonlinear effects in isomeric compounds?The differences among RE cations go beyond simple considerations of atomic radius; the underlying reasons should be attributed to variations in their electronic structures.Previous researchers have explored and synthesized numerous compounds in this eld.In-depth studies of the electronic structures of different cations can help to uncover the answer to this question.Additionally, the contribution of the 5d and 4f empty orbitals of RE cations plays a crucial role in the conductive bands.By delving into the electronic structures of various anions and selectively substituting RE cations and anions with different 4f and 5d electronic structures based on their distinct structures, blind synthesis of RE-based compounds can be avoided, and hidden treasures within the accumulated knowledge can be uncovered.In contemporary research, the continual progress in theoretical calculations and machine learning plays a pivotal role in the exploration and design of novel materials.When synthesizing RE-based chalcogenides, the substitutability of RE sites with various RE elements is commonly considered, yet synthesis endeavours are oen time-consuming.Consequently, upon successfully synthesizing a particular compound, it becomes important to validate, through theoretical calculations, the generalizability of the synthesis method to other RE elements.Additionally, when investigating isostructural compounds, a judicious approach involves preliminary theoretical analyses to identify RE elements that may exhibit superior performance, guiding subsequent synthesis explorations.
(2) According to Pauling's third and fourth rules, in systems containing more than one type of cation, polyhedra with high oxidation states and low coordination numbers tend to be connected through sharing corners or remain unconnected.The two functional motifs [PS 4 ] and [SiS 4 ], which are benecial in terms of E g , can be taken as examples.Due to the high positive charge and low coordination of the central cations, self-aggregation into highdimensional frameworks becomes challenging under electrostatic rules.Therefore, a common approach for stabilization is to connect them with other polyhedra possessing central cations with lower positive charges and higher coordination.When alkali earth metals or alkali metals bond with these functional motifs, the resulting bonds are primarily ionic in nature.One characteristic of ionic bonds is isotropy, which makes it difficult to restrict the orientation of functional motifs and thus facilitates the formation of a thermodynamically stable centrosymmetric phase.Additionally, the isotropic nature of these bonds leads to low optical anisotropy.The bonding between RE n+ and S 2− is complex, primarily due to the complexity of their respective electronic structures.Furthermore, as different RE n+ engage in bonding, the variability in their individual electronic structures contributes to distinct electron density of states within the system.As a result, this diversity leads to varying responses to external light stimuli.The presence of high-coordination RE cations acts as a binder between polyhedra with high oxidation states and coordination numbers.In these systems, RE cations not only play a role as a structural binder, but also contribute to providing nonlinear optical responses.Therefore, re-examining the structures of different compounds in the database reveals that introducing RE cations to connect previously disordered functional units may have a rejuvenating effect of "old wood meets spring", enhancing performance while adjusting the structure.
(3) The growth of large crystals is necessary.Currently, the major RE-based compounds are tested in the powder state, but the real working state of crystal materials is the single-crystal state.Consequently, in order to satisfy the demands of test accuracy, further test results are needed in the large singlecrystal state, which is also a prerequisite for evaluating the commercialization of NLO materials.

Chemical Science
Review . The fundamental structural components consist of discrete [Sn 4 Se 14 ] tetra-nuclear clusters and [Se 3 ] trimers.The coordination environments of the Eu and Sn atoms in the structure are depicted in Fig. 2b and c.It is worth noting that Guo's group, through literature research and detailed structural analysis, pointed out in their report that the coordination geometry of Sn should be more reasonable for four-foldcoordination and six-fold-coordination, contrary to the 4-and 5-coordination mentioned in Yang's article.Experimental results reveal that Eu 8 Sn 4 Se 20 possesses an indirect E g of 1.33 eV and displays antiferromagnetic-type behaviour.Most signicantly, Eu 8 Sn 4 Se 20 exhibits SHG activity

Fig. 1
Fig. 1 Structures of RE 3 GaS 6 along the c axis with unit cell and discrete [GaS 4 ] polyhedra (blue) outlined.

Fig. 2
Fig. 2 (a) Central projection of Eu 8 Sn 4 Se 20 along the c axis with the unit cell outlined; (b and c) coordination environment of the crystallographically independent Eu atoms and the discrete [Sn 4 Se 14 ] tetranuclear cluster.
, a 2D covalent layer of [M II M IV Q 4 ] 2− is made of tetrahedral [M II Q 4 ] and [M IV Q 4 ] motifs, and further stacks along the a direction with [EuQ 8 ] units occupying the intervals.The geometry of the [EuQ 8 ] units can be viewed as a distorted bicapped trigonal prism.

Fig. 4
Fig. 4 Two classic structural types in the RE 3 M 1−x M IV Q 7 family: (a) La 3 CuSiS 7 -type and (b) La 3 FeGaS 7 -type structures with the unit cell outlined.

Fig. 5
Fig. 5 Structures of EuM II M IV Q 4 (space group: Ama2) along the c axis with the unit cell outlined.

Fig. 6
Fig. 6 Structures of (a) La 2 Ga 2 GeS 8 and (b) Eu 2 Ga 2 GeS 7 along the ac plane with the unit cell outlined.

Fig. 7
Fig. 7 Structure of Ba 2 REM III Q 5 along the bc plane with the unit cell outlined.

Fig. 9 ,
one [M III S 4 ] motif is connected with four other [M III S 4 ] motifs to generate a [M III 5 S 16 ] 17− windmill cluster and further interlink together to form a 2D Cairo pentagonal layer along the c direction.Polyhedral [(La/AE)S 8 ] groups lled in the interlayers to bridge neighbouring layers together to build the overall 3D framework.It should be noted that the 2D Cairo pentagonal layer in LaAEAl 3 S 7 contributes to their excellent optical performance.This includes a large d eff (0.8-1.1 times that of AgGaS 2 ), a broad optical E g of 3.76-3.78eV (the rst known cases to achieve the breakthrough of the "3.5 eV wall" among all RE-based IR-NLO chalcogenides), high LIDTs (approximately 9 times that of AgGaS 2 ), and moderate Dn (0.059 for the Ca-compound and 0.077 for the Sr compound at 2000 nm) for PM.These ndings offer a new structural guidance route for the development of high-performance IR-NLO chalcogenides.2.1.10.RE 2 AE 3 M IV 3 S 12 (RE = La, Pr, Nd, Sm, Gd, Ho, and Er; AE = Sr, Ca; M IV = Si, Ge, and Sn).Currently, a signicant challenge in the eld of IR-NLO is how to effectively combine and select asymmetric functional primitives to achieve NCS structures and strong d eff .In 2023, Wu and co-workers achieved successful synthesis of 29 compounds by combining exible [SnS n ] (n = 5 and 6) functional primitives with highly positively charge-balanced ions, such as RE 3+ and AE 2+ cations.These compounds included 12 NCS thiostannates, RE 2 Sr 3 SnS 12 (space group: Pmc2 1 ), and RE 2 Ca 3 Sn 3 S 12 (space group: P 62m), as well as 17 CS compounds, RE 2 AE 3 Ge 3 S 12 and RE 2 AE 3 Si 3 S 12 , constructed from rigid [GeS 4 ] or [SiS 4 ] tetrahedra. 141,142La 2 Sr 3 M IV 3 S 12 (M IV = Si, Ge), La 2 Ca 3 Sn 3 S 12 , and La 2 Sr 3 Sn 3 S 12 serve as three typical examples to illustrate the inherent structural features of the family (Fig. 10).The structure of La 2 Sr 3 M IV 3 S 12 (M IV = Si, Ge) exhibits isolated [M IV S 4 ] groups, and all the isolated [M IV S 4 ] groups located in the c direction are symmetrical.Additionally, the [LaS 8 ] polyhedra are connected together to generate a 3D framework, while the polyhedral [SrS 7 ] and [SrS 9 ] groups are interconnected to create an isolated triple-chain structure.In the La 2 Ca 3 Sn 3 S 12 structure, La and Ca atoms occupy the same

Fig. 8
Fig. 8 Structure of Ba 4 RE 2 Cd 3 S 10 along the a axis with the unit cell outlined.

Fig. 9
Fig. 9 Structure of LaAEM III 3 S 7 along the b axis with the unit cell outlined.

Fig. 10
Fig. 10 CS-to-NCS structural transformation with varying anionic motifs in the RE 2 AE 3 M IV 3 S 12 family.This figure has been adapted from ref. 142 with permission from Wiley-VCH, copyright 2024.
4 for CS) in a unit cell; (ii) [RES 8 ] dodecahedra connect each other via sharing vertexes to generate the 1D isolated [RES 7 ] n chains (Fig. 12a) in NCS structure, which is different than the 1D [RES 6 ] n chain formed by edge-sharing [RES 8 ] units in the CS structure; (iii) isolated [PS 4 ] motifs link with [RES 8 ] units to produce the 1D [REP 2 S 8 ] 3− chains through sharing faces, edges, and vertexes in the NCS structure, which is distinguished from the interconnections (only edge-sharing) between the [RES 8 ] and [PS 4 ] motifs in the CS structure.In addition, the inherent connection mode between the [RES 8 ] and [PS 4 ] motifs in the K-RE-P V -S system was investigated (Fig. 12b) to evaluate the relationships between local asymmetry and the centrality of the overall network.The survey results indicate that most of them belong to the CS space group, and due to local symmetry, have edge sharing patterns between [RES 8 ] and [PS 4 ] motifs.That is, the CS-to-NCS structural transformation in the K 3 REP 2 S 8 family can be attributed to the RE cation-size effect.Remarkably, NCS K 3 REP 2 S 8 displaying strong PM d eff (1.1-1.4 × AgGaS 2 ) and large optical anisotropy (Dn = 0.084-0.099)were also proven to be promising IR-NLO candidates.The SHG density and dipole moment calculations indicate that the synergistic effect between the [RES 8 ] and [PS 4 ] units creates an inherent NLO origin, which veries that RE-based thiophosphates can be regarded as an excellent research system for exploring novel IR-NLO chalcogenides.

Fig. 12
Fig. 12 (a) Structure of K 3 YP 2 S 8 along the ac plane with the unit cell outlined and (b) comparison on the local coordination modes between [RES 8 ] and [PS 4 ] motifs in the reported K/RE/P(V)/S family.

Fig. 13 (
Fig. 13 (a) Central projection of RE 8 Sb 2 S 15 with the unit cell outlined and (b) coordination environment of crystallographically independent RE atoms.

2 . 3 . 1 .
REBS 3 (RE = La, Ce, Pr, Nd, Sm, and Tb).A new class of NLO materials known as thioborates potentially possesses high LIDTs, diverse structures, large d eff values, and wide optical transmittance.Among them, REBS 3 (RE = La, Ce, Pr, Nd, Sm, and Tb) were rst to be reported by Hunger et al. in 2010, but they required rigorous experimental conditions of high temperature and pressure.[163][164][165][166]Moreover, the samples produced using this method were only polycrystalline powders.Therefore, researchers like Hans-Conrad zur Loye et al. explored a new method using the boron-chalcogen mixture approach, with raw materials including RE 2 O 3 /CeO 2 , B, S, and K 2 S/NaI-CsI

Fig. 14 (
Fig. 14 (a) Structure of La 2 CuSbS 5 along the ab plane with the unit cell outlined; (b) coordination environment of crystallographically independent La atoms.Fig. 15 Structures of (a) RE 4 GaSbS 9 and (b) RE 4 InSbS 9 with the unit cell outlined.

Fig. 16
Fig. 16 Structure of LaBS 3 along the ac plane with the unit cell outlined.

Fig. 17
Fig. 17Structure of Ca 2 RE(BS 3 )(SiS 4 ) along the ab plane with the unit cell outlined.

Fig. 18
Fig. 18 Structure of Eu 2 P 2 S 6 along the bc plane with the unit cell outlined.

Fig. 19
Fig. 19 Structure of KREP 2 Se 6 along the bc plane with the unit cell outlined.

Fig. 20
Fig. 20 Structure of (a) La 6 Cd 0.75 Ga 2 Q 11.5 Cl 2.5 along the ac plane and (b) 3D La/Q/(Q/Cl) network along the ab plane with the unit cell outlined.

2 . 4 . 3 .
Eu 4.5 (B 5 O 9 ) 2 SI.The rst sulde borate to possess NLO activity, Eu 4.5 (B 5 O 9 ) 2 SI, contains I − , S 2− , and borate anions simultaneously.It was synthesized by Guo's group in 2019 as a derivative of Eu 2 B 5 O 9 S using KI as a ux in a solid-state reaction. 176Both Eu 4.5 (B 5 O 9 ) 2 SI and Eu 2 B 5 O 9 S crystallize in the NCS orthorhombic Pnn2 space group, but Eu 2 B 5 O 9 S does not exhibit apparent SHG.Here, we discuss the structure of Eu 4.5 (-B 5 O 9 ) 2 SI in detail.The structure of Eu 4.5 (B 5 O 9 ) 2 SI along the ab plane is displayed in Fig. 22a.It consists of a 3D polyanionic network {(B 5 O 9 ) 3− } N , which is constructed by linking 3 [BO 4 ] tetrahedra with 2 [BO 3 ] planar triangles through shared O atoms.Along the c axis, there is a tubular accumulation [Eu 2 (B 5 O 9 )] N framework built by Eu 1 and Eu 2 located in the cavities of the 3D network.The cavities of the 3D network are also occupied by I − ions.Fig. 22b shows the coordination environment of the crystallographically independent Eu atoms, which have three different coordination modes: [Eu 1 O 5 S 2 I], [Eu 2 O 5 S 2 I], and [Eu 3 O 4 S 2 ].The combination of Eu 2+ , S 2− , I − , and borates allows for the realization of a large d eff and a high LIDT.Eu 4.5 (B 5 O 9 ) 2 SI has an E g of 1.99 eV, a moderate d eff of 0.5 × AgGaS 2 , a high LIDT of 15 × AgGaS 2 , and PM behaviour.These results indicate that the Eu-S and B-O motifs play an important role in the d eff and offer an example of the practicality of this strategy.2.4.4.(K 3 I)[REB 12 (GaS 4 ) 3 ] (RE = Sm, Gd).The crystal structure of (K 3 I)[SmB 12 (GaS 4 ) 3 ], which was reported by Guo's group in 2009, represents the rst salt-inclusion chalcogenide

Fig. 21
Fig. 21 Structure of (a) RE 3 AsS 5 X 2 along the ac plane with the unit cell outlined and (b) coordination environment of the crystallographically independent RE atoms.

Fig. 22
Fig. 22 Structure of (a) Eu 4.5 (B 5 O 9 ) 2 SI along the ab plane with the unit cell outlined and (b) coordination environment of the crystallographically independent Eu atoms.
Fig. 25 Structure of YSeBO 2 along the bc plane with the unit cell outlined.

Fig. 26
Fig. 26 Central projection of Eu 3 GeOS 4 along the ac plane with the unit cell outlined.

Fig. 27
Fig. 27 Structure of RE 3 NbS 3 O 4 along the bc plane with the unit cell outlined.

4. 5 ×
AgGaS 2 at 1064 nm.The heteroanionic [NbS 2 O 4 ] unit was rst found as a SHG-active motif, which offers a new route for discovering novel IR-NLO oxychalcogenides.2.4.9.Nd 3 [Ga 3 O 3 S 3 ][Ge 2 O 7 ].Previous studies have shown that it is challenging to achieve chalcogenides based on rare earth (RE) materials that have both a large band gap (E g > 3.5 eV) and a high effective nonlinear optical coefficient (d eff > 0.5 × AgGaS 2 ).However, in 2023, the Zhu research group successfully designed and synthesized a new RE-based oxychalcogenide, Nd 3 [Ga 3 O 3 ][Ge 2 O 7 ], for the rst time. 186This was achieved through a module substitution strategy using the parent structure Cs 3 [Sb 3 O 6 ][Ge 2 O 7 ].Nd 3 [Ga 3 O 3 2 O 7 ] was discovered using the solid-phase method at 1273 K and adopts the hexagonal space group P 62c (no.190).Its unique structure consists of three different modules: charge-balanced Nd 3+ cations, 0D [Ge 2 O 7 ] 6− dimers, and 1D [Ga 3 O 3 S 3 ] 3− tubular chains (Fig. 28).The Nd 3+ cation is coordinated with O/S atoms to form a heteroligand [NdO 6 S 2 ] polyhedron.Experimental investigations of Nd 3 [Ga 3 O 3 ][Ge 2 O 7 ] demonstrate that it is the rst RE-based IR-NLO oxychalcogenide, exhibiting excellent optical performance.This includes a strong d eff (ca.0.8 × AgGaS 2 @2050 nm), a large E g (ca.4.35 eV) corresponding to an ultrahigh LIDT of 23 × AgGaS 2 @1064 nm, a wide transparent window (0.25-13.7 mm), and good thermal stability (<1200 K).Detailed theoretical results indicate that the remarkable d eff in Nd 3 [Ga 3 O 3 ][Ge 2 O 7 ] is mainly attributed to the cooperation of heteroanionic [GaO 2 S 2 ] and [NdO 2 S 6 ] functional motifs.This research not only expands the possibilities of IR-NLO families with heteroanionic motifs, but also offers a feasible strategy for the development of other highperformance IR-NLO systems.2.4.10.Eu 2 M II Ge 2 OS 6 (M II = Mn, Fe, and Co).By coupling RE elements with localized f-electrons, d-block transition metals with delocalized d-electrons, and the mixed anion group [GeOS 3 ] with high polarizability, Guo's group successfully obtained the rst melilite-type RE-based oxythiogermanates, Eu 2 M II Ge 2 OS 6 , where M II represents Mn, Fe, and Co, in 2023.These compounds were prepared via high-temperature solid-phase synthesis using KI as a ux. 187Eu 2 M II Ge 2 OS 6 (M II = Mn, Fe, and Co) are isomorphic and grow in a tetragonal NCS P 42 1 m space group.As shown in Fig. 29a, two neighboring [GeOS 3 ] tetrahedra build a dimer, [Ge 2 OS 6 ], by sharing an O atom.Each [Ge 2 OS 6 ] dimer then

Fig. 28
Fig. 28 Structure of Nd 3 [Ga 3 O 3 S 3 ][Ge 2 O 7 ] along the ab plane with unit the cell outlined.

Fig. 29
Fig. 29 Structure of (a) Eu 2 M II Ge 2 OS 6 along the ac plane and (b) the 2D Eu/O/S network along the ab plane with the unit cell outlined.

Fig. 30
Fig. 30 Structure of LaAEGa 3 S 6 O along the ac plane with the unit cell outlined.

a
Scheme 1 Distribution and proportion of NLO activity in different REbased NCS materials.

Table 1
Summary of reported RE-based chalcogenides containing tetrahedral motifs a Experimental value.b Powder sample.c PM = phase-matchability, NPM = nonphase-matchability.d Theoretical value.e N/A = not available.f The maximum temperature of solid-state reaction.© 2024 The Author(s).Published by the Royal Society of Chemistry Chem.Sci., 2024, 15, 5869-5896 | 5887

Table 2
Summary of reported RE-based chalcogenides containing lone-pair-electron motifs e Compound [REQ n ] polyhedra Space group E g a (eV) d eff b (×AgGaS 2 ) LIDT b (×AgGaS 2 ) NPM/PM c Dn d Maximum temperature f Ref. Powder sample.c PM = phase-matchability, NPM = nonphase-matchability.d Theoretical value.e N/A = not available.f The maximum temperature of solid-state reaction.
a Experimental value.b

Table 3
A summary of reported RE-based chalcogenides containing [BS 3 ] and [P 2 Q 6 ] motifs e LIDT (×AgGaS 2 ) b NPM/PM c Dn d Maximum temperature f Ref.
a Experimental value.b Powder sample.c PM = phase-matchability, NPM = nonphase-matchability.d Theoretical value.e N/A = not available.f The maximum temperature of solid-state reaction.

Table 4 A
summary of reported RE-based chalcohalides and oxychalcogenide e